MATHEMATICAL MODELING OF STRENGTH-DEFORMED CONDITION OF PIPE CONCRETE CONSTRUCTIONS AT SUSTAINABLE TEMPERATURE

Abstract

The mathematical modeling of the thermo-stressed state of pipe-concrete structures under conditions of stationary thermal conductivity is carried out. During the study, the most common structural type of TBC was selected and mathematical models of the stress-strain state of TBA under heating conditions were taken into account, taking into account their geometric dimensions and thermophysical characteristics of metal and concrete. The main feature of the TBC study is that the heat exchange in the structure, as well as the corresponding force response, are investigated independently of each other, whereas the problem of fire resistance should be posed as a classical problem of elasticity, taking into account the mutual influence of temperature and mechanical stresses.

In two-layer structures (concrete - metal), the largest radial stresses that occur in concrete work in tension. Tensile stresses occur in the thickness of the outer tube. The stresses occurring on the inner surface of the steel sleeve coincide with the stresses in the concrete. When approaching the outer surface, they decrease and on the surface r = R₂ equal to zero. In the case where the coefficients of linear extension αt (i = 1, 2) are equal to each other, the maximum tensile stresses are reduced within 0≤r≤R₁ .; if νi (i = 1, 2) within 0≤ r≤R₂, the stresses will also decrease. Axial stresses work on compression. They reach maximum value in the outer shell. For equal values αt ₍₁₎ = αt ₍₂₎, the magnitude of the stresses does not change, and at ν₁ = ν₂ the stresses in the metal will decrease. Ring stresses in the region 0≤ r≤R₁ are tensile stresses and in the region R₁≤ r≤R₂ are compression stresses, and the compression stresses are greater than the tensile stresses in concrete. For αt ₍₁₎ = αt ₍₂₎, the stresses in the concrete decrease and for ν₁ = ν_2.